David Cameron wished to exploit the afterglow of the Olympics by going on the US talkshow The Late Show with David Letterman. That is wrong on so many levels. First, when he is on telly in Britain, talking to his own electorate, he never stops banging on about how public spending has to be curbed because state profligacy always causes harm. If he really believed his own schtick, he would be warning the world about the strain that hosting the Olympics puts on the state purse, fretting about the risks that have been taken with UK plc's credit rating and bemoaning the Olympics' lack of a profit motive.

He would also be emphasising the number of British medallists who had been to private schools, as an example of what the dead hand of the state does to competition. (Tricky, admittedly, when China dominated as ever.) And he would be arguing that, if ever there were a lesson in getting off your bottom and getting on with things, whatever the personal challenges you face, then the Paralympians provided that lesson. But he wouldn't dare say any of that, not least because it would sound both nasty and absurd. As it always does.

Second, it is always so ghastly observing the discomfort of people who ought to know better than to confuse being in public life with being a celebrity. Appearing on Letterman is admittedly not quite so egregious as dating a Cheeky Girl – a category error that probably lost Lembit Öpik his parliamentary seat. But the idea that Cameron could not resist the lure of being a foil of a great light entertainer is still excruciating. Politics is not light entertainment, especially not now. How can Cameron be so keen to parade his shallow solipsism? If Rupert Murdoch was ever right about anything, it's that Cameron is a lightweight.

Third, one can't help suspecting that this is all about Boris Johnson. Johnson stole Cameron's thunder as the Olympics drew to a close, and he has made a successful appearance on Letterman. No doubt a number of politicians are cheesed off by Johnson's policy-free popularity. But they attempt to emulate it at their peril. Johnson was already a bit of a star before he entered politics. His success is derived from being Johnson. Cameron's is derived from his posse's cynical machinations within one dying party – the Conservatives – and his all-too-easy manipulation of another that's now dead on its feet – the Lib Dems.

Were Cameron to allow himself to be candidly interviewed about those machiavellian power plays, it would be riveting TV. But that can't happen – the man is a fake. Johnson has a reckless authenticity, to which people respond. Were Cameron to be recklessly authentic, any audience would be disgusted.

Fourth, it is so needy, this yearning many politicians have to be a success in popular culture, down with the cool kids. It's embarrassing when half of a Labour cabinet turns up for the Brit awards – as in 1998, only to see John Prescott soaked by a bucket of iced water from Danbert Nobacon of Chumbawamba. "If John Prescott has the nerve to turn up at events like the Brit awards in a vain attempt to make Labour seem cool and trendy, then he deserves all we can throw at him," said Nobacon. Quite.

And fifth, they never pull it off. It is painful seeing Gordon Brown pretending he gets up in the morning to a blast of Arctic Monkeys. It is rather less painful to see Tricky confirming that if he did hang with Samantha Cameron in Bristol in the 80s, then it made a far bigger impression on her than it did on him. But that's just me.

Much has been made of Cameron's gaffes on Letterman the other night. His Eton and Oxford education was not substantial enough for him to be able to hazard "big chart" as a literal translation of Magna Carta. He confused Rule Britannia with Land of Hope and Glory. It's a fine joke, ambushing a British PM on what's meant to be his specialist subject. But for me, his biggest gaffe was: "I've ended my career here." What a sad expression of Cameron's priorities that supposedly self-deprecating comment was. But, of course, if politics were a vocation for him, not a career, he wouldn't have been on Letterman in the first place. What a self-regarding, vain, little person Cameron is.

It is more true than ever that: "Politics is show business for ugly people." Never in the history of Britain have all the political parties been headed by such young, inexperienced men. It is as if politics has become the reality TV of alumni of the debating society, a fast track to exposure and a chance to hang out with the glamorous people who were too busy partying to bother with such stuff. The TV stars they shove on their committees, the celebrity businessmen co-opted into working parties, the guest lists they assemble for their country weekends, all of it speaks of a political culture that does not believe politics is where the people with something to offer can be found.

Political commentator Steve Richards does an excellent stand-up routine in which he asks why there is a sense abroad that the politics of his youth was dominated by Big Beasts while the politics of today is peopled by Little Creatures. He doesn't answer the question – Richards loves politics and politicians. He even starts his routine by admitting that, as a schoolboy, he turned down tickets to see David Bowie because he was going to see Harold Wilson. But that's what's wrong with politics today – many ambitious politicians would not have made the same choice as Richards. They are star-struck people who love meeting the heroes of popular culture because they imagine it reflects well on them.

In part, this erosion of the seriousness and centrality of politics can be put down to the intensified power of the media – the scrutiny, the demand for electronically facilitated "connection", the reductio ad absurdum that celebrity culture has imposed on all in the public eye. (Not to mention the reluctance of politicians to challenge any of it, until they were forced to.) But much more importantly, it is due to a decline in belief among politicians themselves in politics as the primary organising force in society.

Since the 1980s, politicians have been eager to persuade people not of what they can achieve, but of what they cannot achieve. In a real sense, many of today's politicians are entryists, going into politics precisely because they do not believe people like them should be running things. This is true to varying degrees of all three parties, but for Cameron and his party, it is the only agenda, the only goal. None of them is willing to talk honestly about the implications of that monstrous project in public. Not when they can move it along so marvellously by going on a chatshow and displaying their limited ability to banter instead.